X-maximal congruences and relevant sets for algebras

• Autorzy: Staruch B. , Staruch B.

Identyfikatory

DOI

10.16926/m.2016.21.08

• Języki publikacji: EN

Abstrakty

EN

We introduce and investigate X-maximal congruences and relevant sets for a given algebra. We describe interrelations among these concepts and atomicity of the congruence lattice and the number of atoms. We also investigate subdirect decomposition of algebras into subdirectly irreducible factors.

Słowa kluczowe

EN

atomicity; Birkhoff theorem; congruence grid; properties of convergent grid

PL

atomowość; właściwości siatki bieżnej; twierdzenie Birkhoffa; siatka zgodności

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2016
• Tom: Vol. 21
• Strony: 93--104
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Staruch B.

• University of Warmia and Mazury, Olsztyn, Poland, Department of Mathematics and Computer Science, ul. Słoneczna 54, 10-710 Olsztyn, Poland

autor

Staruch B.

• University of Warmia and Mazury, Department of Mathematics and Computer Science, ul. Słoneczna 54, 10-710 Olsztyn, Poland

Bibliografia

• [1] Birkhoff, G.: On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31, 433-454, (1935). DOI: 10.1017/S0305004100013463
• [2] Burris, S.; Sankappanavar, H. P. A Course in Universal Algebra, Springer-Verlag, (1981)
• [3] Grätzer, G.: The order of principal congruences of a bounded lattice. Algebra Universalis. 70(1), 95–105 (2013). DOI:10.1007/s00012-013-0242-3
• [4] Grätzer, G.: General Lattice Theory. Second edition. Birkhauser Verlag, Basel (1998).
• [5] Grätzer, G. , Wehrung F. eds.: Lattice Theory: Special Topics and Applications, Vol. 1. Birkhauser Verlag, Basel (2014)
• [6] Staruch Bożena: Extensions of Partial Structures and Their Application to Modelling of Multiagent Systems. In: Monitoring, Security, and Rescue Techniques in Multiagent Systems. Part 1. Advances in Soft Computing Vol. 28., South-Holland, Rotterdam, 293–304 (2005)
• [7] Staruch Bożena, Staruch Bogdan: First Order Theories for Partial Models, Studia Logica, 80(1), 105–120 (2005). DOI: 10.1007/s11225-005-6779-1
• [8] Staruch Bożena, Staruch Bogdan: Maximal congruences for partial structures. Paper presented at the 50th Summer School on General Algebra and Ordered Sets, Matej Bel University in Banska Bystrica, Novy Smokovec, 2–7 September (2012)